Toric duality as Seiberg duality and brane diamonds

By Bo Feng, A. Hanany, Yang-Hui He, A. Uranga. 2001

210 citations recorded by the source corpus.

We use fleld theory and brane diamond techniques to demonstrate that Toric Duality is Seiberg duality for N = 1 theories with toric moduli spaces. This resolves the puzzle concerning the physical meaning of Toric Duality as proposed in our earlier work. Furthermore, using this strong connection we arrive at three new phases which can not be thus far obtained by the so-called \Inverse Algorithm" applied to partial resolution of C 3 =(Z3£ Z3). The standing proposals of Seiberg duality as diamond duality in the work by Aganagic-Karch-Lare strongly supported and new diamond conflgurations for these singularities are obtained as a byproduct. We also make some remarks about the relationships between Seiberg duality and Picard-Lefschetz monodromy.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/054fe78a90f991d0e5f28190b7069a1ee53070aa

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Citations in the corpus

Counting BPS operators in gauge theories: quivers, syzygies and plethystics (2006, background): “Interesting duality structures of these theories have been expounded in [12, 13, 14, 15].”
Derived equivalences from mutations of quivers with potential (2009, background): “3 of [6], Section 6 of [15] and Section 3 of [35].”
Seiberg Duality for Quiver Gauge Theories (2002, methodology): “Recently, several groups [6, 13, 29] have shown that Seiberg dual pairs or even sets of theories can be obtained in this framework, using the procedure of “partial resolution” [50].”
A categorification of Grassmannian cluster algebras (2013, background): “ no cluster variables, of degree d>2. Note that the case k= 1 is of trivial cluster type, with all ncoordinates frozen. For k= 3, the roots of degree 2 are the weights of Λ6(Cn), while for (k,n) = (3,8), the roots of degree 3 are the weights of C8 ⊗Λ8(C8). There are no roots of degree d>4. Com”
Dimer models and toric diagrams (2005, background): “The non-uniqueness phenomenon is called “Toric duality” [9] and is found to be equivalent to Seiberg duality [10, 11, 12].”
Symmetries of Toric Duality (2002, methodology): “This is of course the same as the one given in [9, 8].”
A Geometric unification of dualities (2001, methodology): “7 An important ingredient here, compared to those studied in [21] is the brane creation effect discussed in [19].”
Quivers, tilings, branes and rhombi (2005, background): “These “phases” of the theory are believed to be Seiberg–dual to each other [55, 56, 57, 58].”
Dimer models from mirror symmetry and quivering amoebae (2005, methodology): “As illustrative examples, we draw in figure 7 the zig-zag paths associated to the two dimer models describing quiver theories for the CY cone over P1 × P1, which are related by Seiberg duality [10, 30].”
From Sasaki-Einstein spaces to quivers via BPS geodesics: Lp,q|r (2005, background): “These setups significantly generalize previously known constructions [32, 33, 34, 8].”
THE MASTER SPACE OF N=1 GAUGE THEORIES (2008, background): “There are two toric/Seiberg (see for example [32, 33]) dual phases, (F0)I and (F0)II, of the gauge theory [5], and the quivers and superpotentials are:”
Brane dimers and quiver gauge theories (2005, background): “” Brane diamonds were also applied to the study of gauge theories for D-branes probing complex cones over del Pezzo surfaces [22].”
Fractional branes and dynamical supersymmetry breaking (2005, background): “7.1 Brane tiling perspective of fractional branes 30 7.2 Beta function relations and baryonic U(1) symmetries from brane tilings 35”